Graduate Aptitude Test in Engineering (GATE) — Questions and Answers

Question 1: Which field studies the behavior of forces on structures?

Structural mechanics (Correct answer)
Thermodynamics
Fluid mechanics
Quantum physics

Correct answer: Structural mechanics

Structural mechanics is a specialized field within applied mechanics that focuses on analyzing the behavior of physical structures and their components under various loads and forces. It investigates how structures deform, experience stress, and strain to ensure their stability, strength, and rigidity. This discipline is crucial for the design and analysis of buildings, bridges, and other engineered systems.

Question 2: Which Boolean expression represents the output of an XNOR gate with inputs A and B?

A·B + A'·B' (Correct answer)
A·B'
A'+B'
A⊕B

Correct answer: A·B + A'·B'

XNOR outputs 1 when both inputs are equal, expressed as A·B + A'·B'.

Question 3: Why is continuing education important in Control Systems?

It is not important after certification
Only for re-certification requirements
To stay current with evolving standards and practices (Correct answer)
To network only

Correct answer: To stay current with evolving standards and practices

Continuing education keeps professionals updated with the latest developments, standards, and best practices in their field.

Question 4: Which of the following is a universal gate?

NAND (Correct answer)
OR
AND
XOR

Correct answer: NAND

NAND (and NOR) are universal gates because any Boolean function can be implemented using only NAND gates.

Question 5: Which law explains the relationship between voltage, current, and resistance?

Kirchhoff's Law
Ohm's Law (Correct answer)
Newton's Law
Hooke's Law

Correct answer: Ohm's Law

Ohm's Law describes the fundamental relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. This relationship is mathematically expressed as V = IR, making it essential for electrical engineering and circuit analysis.

Question 6: A token ring network with 4 stations has a token rotation time of 40 ms. If each station transmits for at most 10 ms, what is the maximum efficiency?

50% (Correct answer)
100%
75%
25%

Correct answer: 50%

With 4 stations each transmitting 10 ms in a 40 ms rotation, total transmission = 40 ms, but overhead means efficiency = 4×10/(4×10 + token overhead); assuming 40 ms total cycle, efficiency = 40/80 = 50%.

Question 7: Which algorithmic paradigm is used to efficiently solve the Longest Common Subsequence (LCS) problem?

Dynamic Programming (Correct answer)
Greedy
Backtracking
Divide and Conquer

Correct answer: Dynamic Programming

LCS exhibits optimal substructure and overlapping subproblems, so dynamic programming fills a 2D table in O(m×n) time rather than recomputing subproblems recursively.

Question 8: P is taller than Q. R is taller than P. S is shorter than R but taller than Q. Who is the shortest?

P
R
Q (Correct answer)
S

Correct answer: Q

Order: R>P>S>Q (since S>Q and P>Q and R>P>Q); Q is shortest.

Question 9: The Z-transform of a unit step sequence u[n] is:

z/(z+1) for |z| > 1
z/(z-1) for |z| > 1 (Correct answer)
1/z for |z| > 1
1/(z-1) for |z| > 1

Correct answer: z/(z-1) for |z| > 1

The Z-transform of u[n] = Σ z^(-n) for n≥0 sums to z/(z-1), valid for |z| > 1.

Question 10: What is the worst-case time complexity of QuickSort?

O(n³)
O(n²) (Correct answer)
O(n log n)
O(n log² n)

Correct answer: O(n²)

QuickSort's worst case occurs when the pivot is always the minimum or maximum element (e.g., already-sorted input with a fixed pivot), producing unbalanced partitions and O(n²) comparisons.

Question 11: The minimum number of NAND gates required to implement the function F = A·B + C is:

5
2
3 (Correct answer)
4

Correct answer: 3

F = A·B + C can be realized with 3 NAND gates: NAND(A,B), NAND(C,C), and NAND of their outputs.

Question 12: A sphere of radius r is inscribed in a cube. What is the ratio of the volume of the cube to the volume of the sphere?

π/3
6/π (Correct answer)
3/π
π/6

Correct answer: 6/π

Cube side = 2r; V_cube=(2r)³=8r³; V_sphere=4πr³/3; ratio=8r³/(4πr³/3)=6/π.

Question 13: Which of the following is NOT a characteristic of UDP?

Guaranteed in-order delivery (Correct answer)
Unreliable delivery
Low overhead
Connectionless

Correct answer: Guaranteed in-order delivery

UDP is connectionless and does not guarantee ordered or reliable delivery; guaranteed in-order delivery is a TCP feature.

Question 14: Given relation R(A,B,C,D) with FDs {A→B, B→C, C→D}, which is the highest normal form R is in if A is the only key?

3NF
2NF (Correct answer)
BCNF
1NF

Correct answer: 2NF

B→C and C→D are transitive dependencies on the key A, so R violates 3NF and is only in 2NF (no partial key dependencies exist since the key is single-attribute).

Question 15: Which relational algebra expression represents the SQL: SELECT A FROM R WHERE B = 5?

σ_{B=5}(π_A(R))
π_A(σ_{B=5}(R)) (Correct answer)
σ_A(π_{B=5}(R))
π_B(σ_{A=5}(R))

Correct answer: π_A(σ_{B=5}(R))

First apply selection to filter rows (σ_{B=5}), then apply projection to keep only column A (π_A).

Question 16: Which of the following is NOT a property of a Poisson distribution?

Describes rare event counts in a fixed interval
Events occur independently
The distribution is symmetric about the mean (Correct answer)
Mean equals variance

Correct answer: The distribution is symmetric about the mean

Poisson distributions are right-skewed (not symmetric), though they approach symmetry as λ → ∞.

Question 17: Which flip-flop is commonly used as the basic building block in shift registers?

T flip-flop
D flip-flop (Correct answer)
SR flip-flop
JK flip-flop

Correct answer: D flip-flop

D flip-flops are the standard choice for shift registers because the output directly follows the D input on each clock edge.

Question 18: What is the next term in the letter series: AZ, BY, CX, DW, __?

EV (Correct answer)
FU
EU
FV

Correct answer: EV

First letters A,B,C,D,E (forward); second letters Z,Y,X,W,V (backward); next pair is EV.

Question 19: A train travels 60 miles in 1.5 hours. What is its average speed?

40 mph (Correct answer)
45 mph
50 mph
30 mph

Correct answer: 40 mph

To find the average speed, you divide the total distance traveled by the total time taken. In this case, the train travels 60 miles in 1.5 hours. Therefore, the average speed is calculated as 60 miles / 1.5 hours = 40 miles per hour (mph).

Question 20: Which of the following correctly describes a tri-state buffer?

Outputs only 0 or 1
Has three input lines
Can output 0, 1, or high-impedance (Correct answer)
Always inverts the input

Correct answer: Can output 0, 1, or high-impedance

A tri-state buffer outputs logic 0, logic 1, or high-impedance (Z) depending on its enable signal.

Question 21: A function f(x,y) has a saddle point at (a,b) if the second-order test gives D = f_xx·f_yy - (f_xy)² equal to:

D < 0 (Correct answer)
D = 0
D > 0 and f_xx > 0
D > 0 and f_xx < 0

Correct answer: D < 0

When D < 0, the critical point is a saddle point (neither a maximum nor minimum).

Question 22: Which of the following is a second-order differential equation?

y = mx + c
d²y/dx² = 3x (Correct answer)
∫x dx
dy/dx = x^2

Correct answer: d²y/dx² = 3x

The order of a differential equation is determined by the highest derivative present in the equation. In the equation d²y/dx² = 3x, the highest derivative is the second derivative (d²y/dx²). Therefore, this equation is classified as a second-order differential equation.

Question 23: What is the minimum number of flip-flops needed to build a MOD-10 counter?

3
10
4 (Correct answer)
5

Correct answer: 4

MOD-10 requires 10 states; since 2^3=8 < 10 ≤ 2^4=16, at least 4 flip-flops are needed.

Question 24: The Reynolds number for pipe flow is defined as:

ρV²/μD
ρD/μV
ρVD/μ (Correct answer)
μVD/ρ

Correct answer: ρVD/μ

Reynolds number Re = ρVD/μ = inertial forces/viscous forces, where D is pipe diameter.

Question 25: What is a zero-day vulnerability?

A vulnerability that was fixed immediately
An outdated software version
A low-risk security issue
A security flaw unknown to the vendor with no available patch (Correct answer)

Correct answer: A security flaw unknown to the vendor with no available patch

Zero-day vulnerabilities are newly discovered security flaws that the vendor doesn't know about yet, giving them 'zero days' to fix it before potential exploitation.

Question 26: A project has tasks A, B, C, D with durations 3, 2, 4, 1 days. B depends on A; C depends on A; D depends on B and C. What is the minimum project duration?

8 days (Correct answer)
10 days
9 days
7 days

Correct answer: 8 days

Critical path: A(3) → C(4) → D(1) = 8 days, which is longer than A(3) → B(2) → D(1) = 6 days.

Question 27: Which disk scheduling algorithm minimizes seek time by serving the closest request first?

SSTF (Shortest Seek Time First) (Correct answer)
FCFS
C-SCAN
SCAN

Correct answer: SSTF (Shortest Seek Time First)

SSTF selects the pending request closest to the current disk head position, minimizing individual seek times but potentially causing starvation.

Question 28: Which scheduling algorithm can cause starvation of low-priority processes?

Priority Scheduling (Correct answer)
Round Robin
FCFS
Shortest Job First (non-preemptive)

Correct answer: Priority Scheduling

Priority Scheduling can starve low-priority processes indefinitely if high-priority processes keep arriving.

Question 29: A clock shows 3:15. What is the angle between the hour and minute hands?

15°
0°
7.5° (Correct answer)
22.5°

Correct answer: 7.5°

At 3:15, minute hand is at 90°; hour hand is at 90+15×0.5=97.5°; angle=97.5−90=7.5°.

Question 30: Which of the following is a necessary condition for a maximum of f(x) at x=c?

f''(c) < 0
f(c) > 0
f'(c) = 0 (Correct answer)
f'(c) > 0

Correct answer: f'(c) = 0

f'(c) = 0 is a necessary condition (stationary point), though not sufficient to confirm a maximum.

Question 31: The Mason's gain formula is used to find:

Transfer function from a signal flow graph (Correct answer)
Characteristic roots of a system
Controllability of a state-space system
Stability margins from a Bode plot

Correct answer: Transfer function from a signal flow graph

Mason's gain formula computes the overall transfer function of a signal flow graph using forward paths, loops, and cofactors.

Question 32: What is the amortized time complexity of a single push or pop operation on a dynamic array that doubles in size when full?

O(n)
O(log n)
O(n log n)
O(1) (Correct answer)

Correct answer: O(1)

Doubling doubles the capacity but the total copying cost over all insertions sums to O(n), so by the aggregate method each operation costs O(1) amortized.

Question 33: What role does ethics play in Control Systems practice?

Ethics is optional in professional settings
It only matters for legal compliance
It only applies to managers
It guides professional conduct and protects stakeholders (Correct answer)

Correct answer: It guides professional conduct and protects stakeholders

Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.

Question 34: In two's complement representation, what is −5 in 4 bits?

0101
1101
1010
1011 (Correct answer)

Correct answer: 1011

+5 is 0101; inverting gives 1010, adding 1 gives 1011, which is −5 in two's complement.

Question 35: In probability, what does a cumulative distribution function (CDF) represent?

Probability mass
Mean of a distribution
Cumulative probability up to a value (Correct answer)
Probability density

Correct answer: Cumulative probability up to a value

In probability theory, a cumulative distribution function (CDF) represents the probability that a random variable X will take a value less than or equal to a specific value x. It essentially accumulates the probabilities from the lowest possible value up to x. The CDF provides a comprehensive view of the probability distribution, showing the likelihood of observing values within a certain range.

Question 36: Which page replacement algorithm suffers from Belady's anomaly?

LRU
Clock
FIFO (Correct answer)
Optimal

Correct answer: FIFO

FIFO can paradoxically increase page faults when more frames are added, a phenomenon known as Belady's anomaly.

Question 37: A schedule is conflict-serializable if and only if its precedence graph (conflict graph) is:

Acyclic (Correct answer)
Complete
Connected
Bipartite

Correct answer: Acyclic

A schedule is conflict-serializable if and only if the precedence graph constructed from conflicting operations contains no cycles.

Question 38: What is the Laplace transform of 1?

s^2
s
1/s (Correct answer)
s+1

Correct answer: 1/s

The Laplace transform is an integral transform that converts a function of a real variable (often time, t) into a function of a complex variable (frequency, s). For the constant function f(t) = 1, its Laplace transform is 1/s. This is a fundamental result used extensively in solving linear differential equations and analyzing systems in engineering.

Question 39: The eigenvalues of the matrix [[2, 1], [0, 3]] are:

0 and 3
1 and 3
2 and 3 (Correct answer)
1 and 2

Correct answer: 2 and 3

For an upper triangular matrix, the eigenvalues are the diagonal elements: 2 and 3.

Question 40: In virtual memory, what does the Translation Lookaside Buffer (TLB) store?

Physical memory pages
Free frame list
Page table entries for recently accessed pages (Correct answer)
Disk block addresses

Correct answer: Page table entries for recently accessed pages

The TLB is a hardware cache that stores recent virtual-to-physical page table mappings to speed up address translation.

Question 41: What role does ethics play in Signal Processing practice?

Ethics is optional in professional settings
It only applies to managers
It only matters for legal compliance
It guides professional conduct and protects stakeholders (Correct answer)

Correct answer: It guides professional conduct and protects stakeholders

Professional ethics provide frameworks for responsible decision-making, ensuring practitioners act in the best interest of those they serve.

Question 42: The decimal number 45 in BCD (Binary Coded Decimal) is represented as:

1010 1011
0010 1101
0100 1001
0100 0101 (Correct answer)

Correct answer: 0100 0101

BCD encodes each decimal digit separately: 4 = 0100, 5 = 0101, giving 0100 0101.

Question 43: In a class, 40% students passed in Math, 50% in English, and 20% passed in both. What percentage failed in both?

20%
70%
10%
30% (Correct answer)

Correct answer: 30%

Passed in at least one = 40+50−20 = 70%; failed in both = 100−70 = 30%.

Question 44: A relation R has 3 candidate keys. The minimum number of superkeys R must have is:

7
3
At least 7 (Correct answer)
4

Correct answer: At least 7

Every superset of a candidate key is also a superkey, so with 3 candidate keys the count depends on attribute count but is at least 7 (3 keys + their unions).

Question 45: A 10% increase followed by a 10% decrease results in a net change of:

0%
+1%
-2%
-1% (Correct answer)

Correct answer: -1%

Net multiplier = 1.10 × 0.90 = 0.99, which is a 1% net decrease.

Question 46: In the time-domain analysis of a second-order system, the settling time (2% criterion) is approximately:

π / ωd
4 / (ζωn) (Correct answer)
1 / (ζωn)
2π / ωd

Correct answer: 4 / (ζωn)

The 2% settling time is approximately ts ≈ 4/(ζωn), derived from the envelope of the exponentially decaying oscillation.

Question 47: Choose the word most opposite in meaning to CANDID.

Blunt
Honest
Frank
Evasive (Correct answer)

Correct answer: Evasive

Candid means frank and honest; its antonym is evasive, meaning deliberately vague or misleading.

Question 48: In a Gaussian elimination, partial pivoting is used to:

Speed up computation
Reduce round-off errors by choosing the largest pivot (Correct answer)
Minimize memory usage
Avoid computing inverses

Correct answer: Reduce round-off errors by choosing the largest pivot

Partial pivoting selects the largest available element as pivot to improve numerical stability and reduce round-off errors.

Question 49: The number of asymptotes in the root locus of a system with 4 poles and 1 zero is:

4
5
3 (Correct answer)
1

Correct answer: 3

The number of asymptotes equals P - Z = 4 - 1 = 3, where P is the number of poles and Z is the number of zeros.

Question 50: What is the key difference between a process and a thread?

Processes are lighter weight than threads
Threads cannot run concurrently; processes can
Threads have their own address space; processes share one
Processes have their own address space; threads share it within a process (Correct answer)

Correct answer: Processes have their own address space; threads share it within a process

Each process has its own independent address space, while threads within a process share the same address space and resources.

Question 51: For a causal LTI system, which condition must the region of convergence (ROC) of its z-transform satisfy?

ROC extends to infinity (includes |z| = ∞) (Correct answer)
ROC is the entire z-plane
ROC is a ring in the z-plane
ROC includes the origin

Correct answer: ROC extends to infinity (includes |z| = ∞)

For a causal (right-sided) sequence, the ROC is of the form |z| > r and must include |z| = ∞.

Question 52: Which of the following correctly describes a full-duplex communication channel?

Data flows in one direction only
Data flows in both directions simultaneously (Correct answer)
Data flows in both directions but not simultaneously
Data is broadcast to all nodes

Correct answer: Data flows in both directions simultaneously

Full-duplex allows simultaneous bidirectional data transmission, as opposed to half-duplex which requires turn-taking.

Question 53: If 20% of a number is 80, what is 35% of that number?

140 (Correct answer)
130
120
150

Correct answer: 140

Number = 80/0.20 = 400; 35% of 400 = 140.

Question 54: In modular arithmetic, what is (17 × 23) mod 5?

4
3
1 (Correct answer)
2

Correct answer: 1

17 mod 5 = 2 and 23 mod 5 = 3; so (2 × 3) mod 5 = 6 mod 5 = 1.

Question 55: Which normal form eliminates transitive dependencies in a relation?

3NF (Correct answer)
BCNF
2NF
1NF

Correct answer: 3NF

3NF removes transitive dependencies where a non-key attribute depends on another non-key attribute.

Question 56: A system is said to be observable if:

The transfer function has no RHP zeros
The initial state can be determined from the output over a finite time interval (Correct answer)
All eigenvalues are in the left half-plane
All states can be driven to zero by a suitable input

Correct answer: The initial state can be determined from the output over a finite time interval

Observability means the initial state x(0) can be uniquely determined from the output y(t) over a finite time interval [0, T].

Question 57: The phase margin of a system is defined as 180° plus the phase angle of the open-loop transfer function at:

Gain crossover frequency (Correct answer)
Phase crossover frequency
Bandwidth frequency
Natural frequency

Correct answer: Gain crossover frequency

Phase margin = 180° + ∠G(jωgc)H(jωgc), where ωgc is the gain crossover frequency where |GH| = 1 (0 dB).

Question 58: A train 150 m long passes a pole in 15 seconds. How long will it take to pass a platform 300 m long?

60 seconds
25 seconds
30 seconds
45 seconds (Correct answer)

Correct answer: 45 seconds

Speed = 150/15 = 10 m/s; total distance = 150+300 = 450 m; time = 450/10 = 45 seconds.

Question 59: Which of the following is NOT a condition for deadlock?

Mutual exclusion
Hold and wait
Preemption (Correct answer)
Circular wait

Correct answer: Preemption

Preemption (allowing resources to be forcibly taken) prevents deadlock; the four necessary conditions are mutual exclusion, hold-and-wait, no preemption, and circular wait.

Question 60: In the method of least squares for curve fitting, the objective is to minimize:

The sum of residuals
The sum of absolute residuals
The maximum residual
The sum of squared residuals (Correct answer)

Correct answer: The sum of squared residuals

Least squares minimizes Σ(yᵢ - ŷᵢ)², the sum of squared differences between observed and fitted values.

Question 61: The concept of 'data independence' in DBMS most directly refers to:

Making data accessible without any query language
Encrypting data so applications cannot read raw storage
Storing data on independent disks for redundancy
Ability to change the schema at one level without affecting higher levels (Correct answer)

Correct answer: Ability to change the schema at one level without affecting higher levels

Data independence allows changes to physical or logical schema without requiring application code changes, enabled by the three-level ANSI/SPARC architecture.

Question 62: The complement of (A+B)·C using De Morgan's theorem is:

A'·B'+C' (Correct answer)
(A'+B')·C'
(A·B)+C'
A'·B'·C'

Correct answer: A'·B'+C'

Applying De Morgan's twice: [(A+B)·C]' = (A+B)' + C' = A'·B' + C'.

Question 63: What is the relationship between theory and practice in Signal Processing?

Theory provides the foundation; practice applies it to real situations (Correct answer)
Theory is unnecessary
Practice is unnecessary if you know theory
They are completely separate

Correct answer: Theory provides the foundation; practice applies it to real situations

Theory provides the conceptual foundation and principles, while practice involves applying those concepts to real-world situations. Both are essential for competence.

Question 64: A sentence with a grammatical error: 'The committee have decided to postpone their meeting.' Choose the correction.

No error exists.
The committee has decided to postpone their meeting.
The committee have decided to postpone its meeting.
The committee has decided to postpone its meeting. (Correct answer)

Correct answer: The committee has decided to postpone its meeting.

'Committee' is a collective noun treated as singular in American English, requiring 'has' and the singular pronoun 'its'.

Question 65: In a simply supported beam with a central point load P and span L, the maximum bending moment is:

PL
PL/2
PL/8
PL/4 (Correct answer)

Correct answer: PL/4

For a simply supported beam with central point load P, Mmax = PL/4, occurring at mid-span.

Graduate Aptitude Test in Engineering (GATE)

GATE is a national-level examination in India that primarily tests the comprehensive understanding of various undergraduate subjects in engineering and technology.

Questions

180 min

Time Limit

30%

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